As Google announced at Google I/O 2015 the new Google Cast Remote Display APIs for Android and iOS to make it easy for mobile developers to bring graphically intensive apps or games to Google Cast receivers. Result of it is, Now You can run a classic PC game Quake III now supports Chromecast (when you’re using it with an Android phone or tablet).
Google took an existing Android port of the Quake III Arena open source engine, tweaked it to work with a Chromecast, and ended up with a solution that lets you run the 1999 3D shooter game on your phone while viewing the action on your TV. You can use your phone as a game controller, but you could also pair a Bluetooth or USB gamepad with your phone for a more PC/console-like gaming experience.
While Google hasn’t released a Quake III for Chromecast app to the Play Store, the company has released the source code it used during a demonstration at Google I/O. You’ll need to compile it yourself and copy game data from Quake III in order to actually play the game.